IES 371
Engineering Management
Chapter 14: Aggregate Planning
Week 13
August 31, 2005
Learning Objectives:
Understand the concepts and methods of aggregate planning
Formulate and solve capacity planning problem
1
Aggregate Plan
Aggregate Plan: A statement of a company’s production
rates, workforce levels, and inventory holding based
on estimates of customer requirements and capacity
limitations
Service Industry


Staffing Plan
Regarding staffs and
labor related factors
Manufacturing Industry


Production Plan
Regarding production
rates and inventory
2
Aggregate Production Planning (APP)

Determines resource capacity to meet
demand

For intermediate time horizon, 6-12 months

Not feasible to build new facility


May be feasible to hire/lay off workers,
overtime, or subcontract
Adjusting capacity OR managing demand
3
How should an aggregate plan fit with other plans?
Business
or annual
plan
Production
or staffing
Plan (Aggregate Plan)
MPS or
workforce
schedule
Figure 14.1
4
Aggregate Plan – Managerial Inputs
Distribution and marketing
Customer needs
Demand forecasts
Competition behavior
Operations
Current machine capacities
Plans for future capacities
Workforce capacities
Current staffing level
Materials
Supplier capabilities
Storage capacity
Materials availability
Aggregate
plan
Engineering
New products
Product design changes
Machine standards
Accounting and finance
Cost data
Financial condition
of firm
Human resources
Labor-market conditions
Training capacity
5
Aggregate Plan – Outputs
Aggressive Alternatives
Complementary
Products
Competitive
Pricing
Reactive Alternatives
Size of
Workforce and
Workforce Adjustment
Inventory
Levels
Aggregate
plan
Production
per month
(in units or $)
Units or dollars
Of Backlogs,
backorders , or
stockout
Units or
dollars
subcontracted
6
Aggregate Planning Objectives

Minimize Costs/Maximize Profits

Maximize Customer Service

Minimize Inventory Investment

Minimize Changes in Production Rates

Minimize Changes in Workforce Levels

Maximize Utilization of Plant and Equipment
7
Demand
Units
Examples of Capacity
Adjustment to Meet
Demand
Time
1.
Producing at a constant rate and using inventory to absorb
fluctuations in demand
2.
Hiring and firing workers to match demand
3.
Maintaining resources for high demand levels
4.
Increase or decrease working hours (overtime and undertime)
Subcontracting work to other firms
Using part-time workers
Providing the service or product at a later time period
(backordering)
5.
6.
7.
8
Planning Strategies

Chase Strategies

PURE
STRATEGIES


Level Strategies



Match demand during the planning horizon by
either
Vary workforce or vary output rate
Maintain a constant workforce level or
constant output rate during the planning
horizon
Constant workforce or constant output rate
Mixed Strategies

Combined several strategies
9
Pure Strategy
Level Production
Chase Demand
Demand
Demand
Production
Units
Units
Production
Time
Time
What are pros / cons of these strategies?
10
TABLE 14.1
PLANNING STRATEGIES FOR AGGREGATE PLANS
Possible Alternatives
during Slack Season
Possible Alternatives
during Peak Season
1. Chase #1: vary workforce
level to match demand
Layoffs
Hiring
2. Chase #2: vary output
rate to match demand
Layoffs, undertime,
vacations
Hiring, overtime,
subcontracting
3. Level #1: constant
workforce level
No layoffs, building
anticipation inventory,
undertime, vacations
No hiring, depleting
anticipation inventory,
overtime, subcontracting,
backorders, stockouts
4. Level #2: constant
output rate
Layoffs, building anticipation inventory,
undertime, vacations
Hiring, depleting anticipation inventory, overtime, subcontracting,
backorders, stockouts
Strategy
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Aggregate Planning Costs





Regular-Time Costs
Overtime Costs
Hiring and
Layoff Costs
Inventory
Holding Costs
Backorder and Stockout Costs
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Ex 1 Candy Company
Given the following costs and quarterly sales forecasts of a candy
company, compare the two strategies:
Strategy 1: Level production with constant workforce level
Strategy 2: Chase production by varying workforce level
Quarter
Spring
Summer
Fall
Winter
Sale Forecast
(LB)
80,000
50,000
120,000
150,000



Hiring cost
Firing cost
Inventory carrying cost
Production rate per
employee
 Beginning workforce

$100 per worker
$500 per worker
$0.50 per pound per
quarter
1000 pounds per
quarter
100 workers
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


A method of LP
Gather all cost info
into one matrix
Try to obtain the
lowest cost alternative
Quarter
Transportation
Method
Alternatives
Quarter
1
2
Beginning
inventory
0
Regular
time
r
Regular
time
Overtime
Subcontract
Regular
time
3
Overtime
Subcontract
Regular
time
3h
4h
r+h
r+2h
r+3h
u
R1
c+h
c+2h
c+3h
0
O1
s
s+h
s+2h
s+3h
0
S1
r+b
r
r+h
r+2h
u
R2
c+b
c
c+h
c+2h
0
O2
s+b
s
s+h
s+2h
0
S2
r+2b
r+b
r
r+h
u
R3
c+2b
c+b
c
c+h
0
O3
s+2b
s+b
s
s+h
0
S3
r+3b
r+2b
r+b
r
u
R4
c+3b
4
2h
Overtime
Subcontract
2
4
I0
c
1
h
3
Unused
Total
Capacity Capacity
c+2b
c+b
c
0
Overtime
O4
s+3b
s+2b
s+b
s
0
Subcontract
S4
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Requirements
D1
D2
D3
D4 + I4
U
Notations
It = inventory at the end of period t (I0 = beginning inventory)
h = holding cost per unit per period,
r = regular production cost per unit,
o = overtime cost per unit,
u = undertime cost per unit
s = subcontracting cost per unit,
b = backordering cost per unit per period
Rt = regular-time capacity in period t
Ot = overtime capacity in period t
St = subcontracting capacity in period t
Dt = forecasted demand for period t
U = total unused capacities
15
Tableau Method



Step 1: Put all capacities from the total capacity column
into the unused capacity column. Next, put unit costs in
each of the small boxes
Step 2: In column 1 (period 1), allocate as much
production as you can to the cell with the lowest cost but
do not exceed the unused capacity in that row or the
demand in that column.
Step 3: Subtract your allocation from the unused capacity
for the row. This quantity must never be negative.
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Tableau Method


(Cont’d)
Step 4: If there is still some demand left, repeat step 2,
allocating as much production as possible to the cell with the
next-to-lowest cost. Repeat until the demand is satisfied.
Step 5: Repeat steps 2 through 4 for periods 2 and beyond. Take
each column separately before proceeding to the next. Be sure to
check all cells with unused capacity for the cell with the lowest
cost in a column.
17
Ex 2: Transportation Method
Given the following costs and quarterly sales forecasts, use
the transportation method to design a production plan.
What is the total cost of the plan?
Quarter
Sale Forecast
(unit)
1
2
3
4
50,000
150,000
200,000
52,000
Inventory carrying cost = $3 per unit per quarter
Production/worker = 1000 units/quarter
Regular workforce = 50 workers
Overtime capacity = 50,000 units
Subcontracting capacity = 40,000 units
Regular production cost = $50/unit
Overtime production cost = $75/unit
Subcontracting cost = $85/unit
18
Linear Programming Model (LP)




Pure/Mixed Strategy: not guarantee optimal solution
LP: can get optimal solution
LP: Excel, LINGO, CPLEX, …
LP Formulation**


Objective function
Constraints
Ex 2: Formulate LP model for Ex 1 Candy Company and Ex 2
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